1. Field of the Invention
The present invention relates to a computer-readable recording medium recording a mask data generation program, a mask data generation method, a mask fabrication method, an exposure method, and a device manufacturing method.
2. Description of the Related Art
There has conventionally been used a projection exposure apparatus, which uses a projection optical system to transfer the circuit pattern drawn on a mask (reticle) onto a substrate (e.g., a wafer). Under the circumstances, a demand for a high-resolution exposure apparatus is increasing. Known high-resolution exposure methods increase the numerical aperture (NA) of a projection optical system, shorten the exposure wavelength (λ), or decrease the k1 factor.
Multiple exposure is one of the micropattern exposure techniques. Multiple exposure includes a method of superimposing latent image patterns after each of a plurality of exposure processes, without executing a development process between them, and a method of executing a development process after each of a plurality of exposure processes. A representative example of the former method is double exposure, in which a dense pattern is divided into two sparse patterns. In another double exposure, a line pattern is divided in vertical and horizontal directions, and the divided patterns are separately transferred by exposure to form a desired line pattern. In the latter method, latent image patterns are superimposed by executing the development process after each exposure process. These methods are one approach to decreasing the k1 factor.
“Proceedings of SPIE Vol. 5853 (2005)”, on page 180, describes how to divide a plurality of elements of a layout pattern. That is, an interference map is calculated to obtain a forbidden pitch on the basis of this map. Then, among the plurality of elements of the layout pattern, an element, which is positioned at a forbidden pitch, is extracted from the plurality of elements and set as another mask pattern. Among the remaining plurality of elements, an element, which is positioned at a forbidden pitch, is extracted from the remaining plurality of elements and set as still another mask pattern as well. Repeating such procedures makes it possible to divide the plurality of elements of the layout pattern so that they become free from any forbidden pitches.
Japanese Patent Laid Open Nos. 2004-221594 and 2005-183981 describe techniques of obtaining an approximate distribution of imaging plane amplitude by numerical calculation to derive an interference map. That is, the interference map expresses an approximate distribution of imaging plane amplitude.
More specifically, a transmission cross coefficient (to be referred to as a TCC hereafter) is derived. An aerial image undergoes decomposition (singular value decomposition; SVD) into N images (called eigenfunctions, N: a Natural number) on the basis of the TCC result. This method is called a sum of coherent system decomposition (to be referred to as SOCS hereafter).
The N eigenfunctions decomposited by SOCS each have a positive or a negative value. An eigenvalue (ith eigenvalue) corresponding to the ith eigenfunction is multiplied by a function obtained by squaring the absolute value of the ith eigenfunction to obtain N functions. The N functions are added to obtain an aerial image.
Assuming that a largest eigenvalue is the first eigenvalue and its corresponding eigenfunction is the first eigenfunction, the first eigenfunction contributes most to forming an aerial image. In view of this, the aerial image is approximated by the first eigenfunction. This approximation allows the derivation of an imaging plane amplitude distribution. That is, an interference map can be calculated.
An auxiliary pattern is inserted in a portion having a positive value in the interference map, such that exposure light transmitted through the contact hole pattern is in phase with that transmitted through the auxiliary pattern. An auxiliary pattern is inserted in a portion having a negative value in the interference map, such that the phase difference between exposure light transmitted through the contact hole pattern and that transmitted through the auxiliary pattern is 180°.
Unfortunately, the techniques described in Japanese Patent Laid-Open Nos. 2004-221594 and 2005-183981 require the calculation of a TCC and eigenfunction to derive an interference map. This often complicates the whole numerical calculation, to result in a long mask data generation time.
In the technique described in “Proceedings of SPIE Vol. 5853 (2005)”, on page 180, mask data for multiple exposure is generated using the interference map. Likewise, this often results in a long mask data generation time.